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On the Gauss map of helicoidal surfaces

김영호|김원용|김동수
대한수학회 (The Korean Mathematical Society)|2017.07|대한수학회논문집 (Communications of the KMS)|제32권 제3호|pp. 715-724

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참고문헌

키워드

Gauss maphelicoidal surfacesLaplace operatorCheng-Yau operator
주제분류수학

초록

We study the Gauss map $G$ of helicoidal surfaces in the 3-dimensional Euclidean space ${\mathbb{E}^3}$ with respect to the so called Cheng-Yau operator $\square$ acting on the functions defined on the surfaces. As a result, we completely classify the helicoidal surfaces with Gauss map $G$ satisfying $\square G=AG$ for some $3\times3$ matrix $A$.

Abstract

We study the Gauss map $G$ of helicoidal surfaces in the 3-dimensional Euclidean space ${\mathbb{E}^3}$ with respect to the so called Cheng-Yau operator $\square$ acting on the functions defined on the surfaces. As a result, we completely classify the helicoidal surfaces with Gauss map $G$ satisfying $\square G=AG$ for some $3\times3$ matrix $A$.

참고문헌 (25)

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관련 논문AI추천

Classifications of helicoidal surfaces with L1-pointwise 1-type Gauss map김영호, Nurettin Cenk Turgay대한수학회 · 대한수학회보2013 · 제50권 제4호Helicoidal surfaces and their Gauss map in Minkowski 3-space II김영호, 최미경, Gi-Chan Park대한수학회 · 대한수학회보2009 · 제46권 제3호HELICOIDAL SURFACES AND THEIR GAUSS MAP IN MINKOWSKI 3-SPACE김영호, 윤대원, 최미경, Huili Liu대한수학회 · 대한수학회보2010 · 제47권 제4호Helicoidal surfaces with pointwise 1-type Gauss map최미경, Dong-Soo Kim, Young Ho Kim대한수학회 · 대한수학회지2009 · 제46권 제1호Cheng-Yau operator and Gauss map of Translation Surfaces김동서, 김동수한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제1호ON POINTWISE 1-TYPE GAUSS MAP OF SURFACES IN E3 1 CONCERNING CHENG-YAU OPERATOR김영호, Nurettin Cenk Turgay대한수학회 · 대한수학회지2017 · 제54권 제2호

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